Q. 125.0( 4 Votes )

If = (a + ib), find the values of a and b.

Answer :

Given:

Consider the given equation,



Now, we rationalize



[Here, we multiply and divide by the conjugate of 1 + i]




Using (a + b)(a – b) = (a2 – b2)




[ i2 = -1]



= (-i)100


= [(-i)4]25


= (i4)25


= (1)25


[ i4 = i2 × i2 = -1 × -1 = 1]


(a + ib) = 1 + 0i


On comparing both the sides, we get


a = 1 and b = 0


hence, the value of a is 1 and b is 0


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